Here's a tool for viewing the text contained in multiplayer replay files. They only record the keys pushed by the player who recorded them, so unless someone sends you their replay.rep file, you will only be able to see your side of the conversation.
To record a replay, create gta2\test folder. Run GTA2 Manager, go to the debug tab, tick "Constant Replay Save" and "Do Release Replay" and then click the quit button or start game button to save the changes.
It's best to run this tool from your gta2\test\ folder since it defaults to the current folder for replays. You can also pass it a replay filename on the command line or drag a replay file onto the chatviewer.exe.http://gtamp.com/GTA2/gta2replaychatviewer.7z
VB6 source code included.
It could be extended to send your in game messages to someone not currently in your game. I believe the network packets are similar, so I should be able to modify it to decode chat contained in packet logs.